# For each value of $t$, find an orthogonal basis of the span of the vectors:

$$u_1 = (1,t,t)$$, $$u_2 = (2t,t+1,2t-1)$$, $$u_3 = (2-2t,t-1,1)$$

Any help would be appreciated, if you could explain how to work such questions out

• Are you familiar with the Gram-Schmidt algorithm? – user512346 Nov 17 '18 at 16:12

Step 1, check if the vectors are independent. In the general case, compute the determinant of the matrix form by the components of your vectors. In this case, just add together $$u_2$$ and $$u_3$$, then notice that it's proportional to $$u_1$$. So you need only two vectors in this case.